Exam-style question
Try this first
In a proof by deduction, which response best shows how a conclusion follows from stated assumptions?.
- A.A1: choose the method that matches the structure of mathematical proof
- B.Use any familiar GCSE calculation even if it ignores the structure of mathematical proof
- C.Write only the final answer without showing the mathematical method
- D.Change the notation or restrictions to make the algebra look simpler
Model answer
What a good answer should say
- The correct answer is A1: choose the method that matches the structure of mathematical proof.
- It is correct because a deductive proof starts from accepted assumptions, applies valid algebraic or logical implications, and ends with the stated conclusion rather than relying on examples.
This answer is tied to the objective: A1 Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof including proof by deduction and proof by exhaustion; use disproof by counter example; use proof by contradiction including proof of the irrationality of sqrt(2), the infinity of primes and application to unfamiliar proofs..
Explanation
Why this works
Use the explanation to connect the worked answer back to A1 Understand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof including proof by deduction and proof by exhaustion; use disproof by counter example; use proof by contradiction including proof of the irrationality of sqrt(2), the infinity of primes and application to unfamiliar proofs..
This A1 item focuses on proof by deduction. The correct option keeps the chain of reasoning visible: assumption, justified implication, and conclusion.
The distractors fail because checking a few values, hiding the method, or changing restrictions cannot establish a general result for every permitted case.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: recall.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.